Profit And Loss
Math MCQs

Question :    John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

Correct Answer  310

Solution & Explanation

Solution

Finding the cost price if the sale price and profit percent are known

The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.

Finding the cost price using the formula when the sale price and profit percent are known

Given, the sale price (SP) = $372

And, the profit = 20%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and profit percent are known

Cost Price (CP) = ¹⁰⁰/_{100 + gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 + 20} × 372

= ^{100 × 372}/₁₂₀

= ³⁷²⁰⁰/₁₂₀ = 310

Thus, the Cost Price (CP) = $310 Answer

Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given

Let the Cost Price (CP) = m

Here given profit = 20%

Calculation of Profit

Profit is calculated on cost price (CP)

Formula to find the Profit = Profit% of CP

Thus, profit on the cost price of m

= 20% of m

= 20% × m

= ²⁰/₁₀₀ × m

⇒ Profit = ^{20 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) + Profit

⇒ 372 = m + ^{20 m}/₁₀₀

⇒ 372 = ^{100 m + 20 m}/₁₀₀

⇒ 372 = ^{120 m}/₁₀₀

After cross multiplication, we get

372 × 100 = 120 m

⇒ 120 m = 372 × 100

⇒ m = ^{372 × 100}/₁₂₀

⇒ m = ³⁷²⁰⁰/₁₂₀ = 310

⇒ m = 310

Thus, the Cost Price (CP) = $310 Answer

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given

Given, the sale price (SP) = $372

And, the profit = 20%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 20% of 100 = 20

Thus, Sale Price (SP) = Cost Price (CP) + Profit

⇒ Sale Price (SP) = 100 + 20

⇒ Sale Price (SP) = 120

∵ If the Sale Price (SP) is 120, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₁₂₀

∴ If the Sale Price (SP) is 372, then the Cost Price (CP)

= ¹⁰⁰/₁₂₀ × 372

= ^{100 × 372}/₁₂₀

= ³⁷²⁰⁰/₁₂₀ = 310

Thus, the Cost Price (CP) = $310 Answer

Shortcut Method to find Cost Price (CP) when SP and profit percent are known

Given, the sale price (SP) = $372

And, the profit = 20%

Then, the Cost Price (CP) = ?

SP = 120% of CP

⇒ SP = ¹²⁰/₁₀₀ × CP

⇒ 372 = ^{120 CP}/₁₀₀

After cross multiplication

⇒ 372 × 100 = 120 CP

⇒ 120 CP = 372 × 100

⇒ CP = ^{372 × 100}/₁₂₀

⇒ CP = ³⁷²⁰⁰/₁₂₀ = 310

⇒ CP = $310 Answer

Similar Questions

(1) Find the cost price, if a share broker gets a loss of 28% by selling 300 shares for $3895.20.

(2) Find the cost price, if a trader gets a loss of 62% by selling 10 TV sets for $4639.80

(3) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

(4) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

(5) Find the cost price, if a trader gets a loss of 42% by selling an article for $4761.80

(6) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(7) Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?

(8) If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

(9) Find the cost price, if a trader gets a loss of 12% by selling some of his stock of fruits for $1944.80. Find the cost price of those stock.

(10) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?